Various processes and apparatus which are in use individually package flat products, typically printed products, by sequentially encasing the printed products, one after the other, within a foil. The operating speed of such apparatus is comparatively slow, even if the machine speed is increased continuously, by optimizing various operating parameters, and by the use of modern, usually electronic control apparatus. The number of wrappings per unit time is limited at the operating stations in which a certain minimum time for transport, positioning, and welding or adhesion together of web or foil material is required. In such instances, various wrapping apparatus or machines must be used in parallel in order to be able to reach a predetermined wrapping output of the overall system. Use of parallel machinery requires substantial financial investments, and also increases the space for the location of the apparatus. Such space is frequently expensive, or may not be available, in which case the overall operating speed of the system is decreased.